(c) and are collinear but not equal they are parallels their direction are not same.
<p><picture><img src="https://images.shiksha.com/mediadata/images/articles/1733475138php3MFCA4.jpeg" alt="" width="193" height="153"></picture></p><p><strong> (a)</strong> Vector <span title="Click to copy mathml"><math><mrow><mover accent="true"><mrow><mi>a</mi></mrow><mo stretchy="true">→</mo></mover></mrow></math></span> and <span title="Click to copy mathml"><math><mrow><mover accent="true"><mrow><mi>d</mi></mrow><mo stretchy="true">→</mo></mover></mrow></math></span> are co initial same initial point.</p><p><strong> (b)</strong> <span title="Click to copy mathml"><math><mrow><mover accent="true"><mrow><mi>b</mi></mrow><mo stretchy="true">→</mo></mover></mrow></math></span> and <span title="Click to copy mathml"><math><mover accent="true"><mrow><mrow><mi>d</mi></mrow></mrow><mo>? </mo></mover><mi></mi><mi></mi></math></span> same magnitude & direction.</p><p><strong> (c)</strong> <span title="Click to copy mathml"><math><mrow><mover accent="true"><mrow><mi>a</mi></mrow><mo stretchy="true">→</mo></mover></mrow></math></span> and <span title="Click to copy mathml"><math><mrow><mover accent="true"><mrow><mi>c</mi></mrow><mo stretchy="true">→</mo></mover></mrow></math></span> are collinear but not equal they are parallels their direction are not same.</p>
|a × b|² + |a . b|² = |a|²|b|² 8² + (a . b)² = 2² * 5² 64 + (a . b)² = 100 (a . b)² = 36 a . b = 6 (since angle seems acute from options, but could be -6).
a = i + j + 2k b = -i + 2j + 3k a + b = 3j + 5k a . b = -1 + 2 + 6 = 7 a × b = |i, j, k; 1, 2; -1, 2, 3| = -i - 5j + 3k (a - b) × b) = (a × b) - (b × b) = a × b (a × (a - b) × b) = a × (a × b) = (a . b)a - (a . a)b = 7a - 6b . The expression becomes (a + b) × (7a - 6b) × b) = (a + b) × (7 (a ×&n
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a = i + j + 2k b = -i + 2j + 3k a + b = 3j + 5k a . b = -1 + 2 + 6 = 7 a × b = |i, j, k; 1, 2; -1, 2, 3| = -i - 5j + 3k (a - b) × b) = (a × b) - (b × b) = a × b (a × (a - b) × b) = a × (a × b) = (a . b)a - (a . a)b = 7a - 6b . The expression becomes (a + b) × (7a - 6b) × b) = (a + b) × (7 (a × b) = 7 [ (a × (a × b) + (b × (a × b) ] = 7 [ (7a - 6b) + (b . b)a - (b . a)b) ] = 7 [ 7a - 6b + 14a - 7b ] = 7 (21a - 13b) This seems overly complex. Let's re-examine the expression provided in the solution image. Let's assume the expression is 7 (3j + 5k) × (-i - 5j + k). |i, j, k; 0, 3, 5; -1, -5, 1| = i (3+25) - j (5) + k (3) = 28i - 5j + 3k. This also differs. The solution provided seems to have a typo in the cross product calculation. Let's assume the question meant (a . b) [ (a+b) × (a-b)×b)] . Let's follow the solution calculation: 7 . |i, j, k; 0, 3, 5; -1, -5, 1| = 7 (34i - 5j + 3k). This is wrong. Correct cross product: 28i - 5j + 3k. Let's assume the vector in the final step is (a × b) as calculated: -i-5j+3k. 7 (3j + 5k) × (-i - 5j + 3k) = 7 (34i - 5j + 3k).
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